I am not aware that find (alone) can do what you are after. Having said that, I think there are two options to achieve what you want:

In case you wanna get rid of the the quoting mechanism and use parts of a file name as the matching criteria, you could use output redirection into a file and then grep that file or, in case you want everything in one command, pipe find's output directly to grep (which I'd prefer). That should not be too slow if you instruct find to only print out the names of files (it would just traverse every directory and print the file names which is actually pretty fast) and let grep do the search for the 'portion of file name' as you have put it. If there's no terminal output involved, this is very fast indeed.

If, on the other hand, you are after more flexibility in the search pattern (like grep's regular expressions) then you could combine

Code:

find -regextype

to set the types of regular expressions that find understands and combine this option with

Code:

find -regex

for case sensitive searches or

Code:

find -iregex

for case insensitive searches.

It's probably worth noting that quoting the search strings is required with grep and find (and also any other command) to protect wildcard characters from being interpreted by the shell before being passed to the command as an argument. So the quoting is not really special to find at all.